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Math Help - rewrite complex number

  1. #1
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    rewrite complex number

    who know how to convert z/(z^2+9) to z/(z+3i)/(z-3i)?i really do not have any idea how the book convert it.
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  2. #2
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    Hello,

    x+9=x-(9i)

    What else ?
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  3. #3
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    no,look carefully at the question,i want to ask why z^2+9=(z+3i)/(z-3i)
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  4. #4
    Moo
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    This is not possible

    Perhaps they meant \frac{\frac{z}{z+3i}}{z-3i} which is \frac{z}{(z+3i)(z-3i)}
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  5. #5
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    thanks,i think you are right.by the way,in another question,i saw it write 1/(z^2+1)=(1/2i)/(z-i) - (1/2i)/(z+i).how they did it?
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  6. #6
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    Woah, it's better when you put the parenthesis where it has to go


    \frac{1}{z^2+1}=\frac{1}{(z-i)(z+i)}=\frac{a+bi}{z-i}+\frac{c+di}{z+i}

    =\frac{(a+bi)(z+i)+(c+di)(z-i)}{z^2+1}

    The numerator has to be equal to 1.

    So develop, then group the terms including z and write that its coefficient must be null since z doesn't appear in "1".
    Solve for a, b, c and d
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